Winning Words–Three Puzzle Cases to Generate a Philosophy Discussion!



Three Problems

Bart Schultz, University of Chicago


An excellent way to begin a philosophy discussion is with a puzzle case, and the following cases have a very successful track record in challenging philosophers of all ages.  They can be adapted for the age groups in question, but the basic lesson plan for each case is simply to present the problem in an engaging fashion and then ask the students what they think or what they would do.  The students should be pressed to give reasons for their views, and the facilitator should seek to clarify how the reasons given relate to various ethical perspectives and principles.


  1. Peter Singer’s Pond:

“To challenge my students to think about the ethics of what we owe to people in need, I ask them to imagine that their route to the university takes them past a shallow pond. One morning, I say to them, you notice a child has fallen in and appears to be drowning. To wade in and pull the child out would be easy but it will mean that you get your clothes wet and muddy, and by the time you go home and change you will have missed your first class.

I then ask the students: do you have any obligation to rescue the child? Unanimously, the students say they do. The importance of saving a child so far outweighs the cost of getting one’s clothes muddy and missing a class, that they refuse to consider it any kind of excuse for not saving the child. Does it make a difference, I ask, that there are other people walking past the pond who would equally be able to rescue the child but are not doing so? No, the students reply, the fact that others are not doing what they ought to do is no reason why I should not do what I ought to do.

Once we are all clear about our obligations to rescue the drowning child in front of us, I ask: would it make any difference if the child were far away, in another country perhaps, but similarly in danger of death, and equally within your means to save, at no great cost – and absolutely no danger – to yourself? Virtually all agree that distance and nationality make no moral difference to the situation. I then point out that we are all in that situation of the person passing the shallow pond: we can all save lives of people, both children and adults, who would otherwise die, and we can do so at a very small cost to us: the cost of a new CD, a shirt or a night out at a restaurant or concert, can mean the difference between life and death to more than one person somewhere in the world – and overseas aid agencies like Oxfam overcome the problem of acting at a distance.

At this point the students raise various practical difficulties. Can we be sure that our donation will really get to the people who need it? Doesn’t most aid get swallowed up in administrative costs, or waste, or downright corruption? Isn’t the real problem the growing world population, and is there any point in saving lives until the problem has been solved? These questions can all be answered: but I also point out that even if a substantial proportion of our donations were wasted, the cost to us of making the donation is so small, compared to the benefits that it provides when it, or some of it, does get through to those who need our help, that we would still be saving lives at a small cost to ourselves – even if aid organizations were much less efficient than they actually are.

I am always struck by how few students challenge the underlying ethics of the idea that we ought to save the lives of strangers when we can do so at relatively little cost to ourselves. At the end of the nineteenth century WH Lecky wrote of human concern as an expanding circle which begins with the individual, then embraces the family and ‘soon the circle… includes first a class, then a nation, then a coalition of nations, then all humanity, and finally, its influence is felt in the dealings of man [sic] with the animal world’.1 On this basis the overwhelming majority of my students seem to be already in the penultimate stage – at least – of Lecky’s expanding circle. There is, of course, for many students and for various reasons a gap between acknowledging what we ought to do, and doing it; but I shall come back to that issue shortly.”—From Peter Singer, “The Drowning Child and the Expanding Circle,”–.htm

For more information, see:


  1. Derek Parfit’s Repugnant Conclusion:

“Parfit is not the first philosopher to have noticed that influential moral views may have implications of the sort outlined in the Repugnant Conclusion. Henry Sidgwick was close to acknowledging the implication when he pointed out that “… the point up to which, on utilitarian principles, population ought to be encouraged to increase, is not that at which the average happiness is the greatest possible—as appears to be often assumed by political economists of the school of Malthus—but that at which the happiness reaches its maximum” (Sidgwick 1907 p. 418; for other early sources, see Broad 1930 pp. 249–250; McTaggart 1927 pp. 452–53; Narveson 1967). However, it is Parfit who has brought the conclusion to recent philosophical attention both by stressing the importance of the conclusion and by showing how difficult it is to avoid it (Parfit 1984).

Parfit was led to the Repugnant Conclusion by his considerations concerning how we ought to act in cases where our decisions have an impact on who will exist in the future. Consider the following two scenarios (see Parfit 1984 chapter 16):

  1. A pregnant mother suffers from an illness which, unless she undergoes a simple treatment, will cause her child to suffer a permanent handicap. If she receives the treatment and is cured her child will be perfectly normal.
  2. A woman suffers from an illness which means that, if she gets pregnant now, her child will suffer from a permanent handicap. If she postpones her pregnancy a few months until she has recovered, her child will be perfectly normal.

What ought the women to do in the two cases? In case (1) the obvious answer is that the mother ought to undergo the treatment since her actual child will thereby get a better life. However, it is problematic to appeal to this kind of reason when we turn to case (2). If the woman postpones her pregnancy, then the child that is brought into existence will not be identical to the child she would have had, had she decided to become pregnant while she was ill (it will not be the same ovum and sperm that meet). Hence, the alternative for the child brought into existence during the mother’s illness is non-existence, and to claim that it would have been better for this child if the mother had postponed pregnancy is tantamount to claiming that non-existence would have been better for her. Assuming that the child has a life worth living, this seems wrong if not nonsensical (for a discussion, see Narveson 1967, Parfit 1984, appendix G; Bykvist 2007; Arrhenius 2009a; McMahan 1981, 2009; Rabinowicz 2009).

How, if at all, should a change in the identity of the involved parties in the compared outcomes affect our moral evaluation? Parfit refers to this as “the Non-identity Problem” (see the entry on the nonidentity problem). Following what would probably strike most people as the most plausible answer Parfit favors what he calls the “No-Difference View” (1984 p. 367), which implies that a change in identity should not affect the answer: the woman in case 2) ought to postpone her pregnancy, just as the woman in case 1) ought to undergo the treatment. A straightforward way of capturing the No-Difference View is the Impersonal Total Principle: If other things are equal, the best outcome is the one in which there would be the greatest quantity of whatever makes life worth living (Parfit 1984 p. 387). However, this view implies that any loss in the quality of lives in a population can be compensated for by a sufficient gain in the quantity of a population; that is, it leads to the Repugnant Conclusion. Consider the following diagram:
Figure 1

The blocks above represent two populations, A and Z. The width of each block shows the number of people in the corresponding population, the height shows their quality of life or welfare. All the lives in the above diagram have lives worth living. People’s quality of life is much lower in Z than in A but, since there are many more people in Z, there is a greater quantity of welfare in Z as compared to A. Consequently, although the people in A lead very good lives and the people in Z have lives only barely worth living, Z is nevertheless better than A. Thus, the attempt to provide a plausible solution to the Non-identity problem has led to a seemingly unacceptable conclusion.

Leaving the mentioned Non-identity case aside, there are other arguments establishing that the Repugnant Conclusion is not easily avoided. Parfit has developed an argument to this effect. Consider the three population scenarios indicated in Fig. 2.
Figure 2

Scenario A contains a population in which everybody leads lives well worth living. In A+ there is one group of people as large as the group in A and with the same high quality of life. But A+ also contains a number of people with a somewhat lower quality of life. In Parfit’s terminology A+ is generated from A by “mere addition”. Comparing A and A+ it is reasonable to hold that A+ is better than A or, at least, not worse. Addition of extra worthwhile lives cannot make an outcome worse. Consider the next scenario B with the same number of people as A+, all leading lives worth living and at an average well-being level slightly above the average in A+, but lower than the average in A. It is hard to deny that B is better than A+ since it is better in regard to both average welfare and equality. However, if A+ is at least not worse than A, and if B is better than A+, then B is also better than A given full comparability among populations (i.e., setting aside possible incomparability among populations). By parity of reasoning (scenario B+ and C, C+ etc.), we end up with a scenario Z where the population has a very low positive quality of life. Thus, the final conclusion is that Z is better than A, which is the Repugnant Conclusion. By what apparently constitute sound steps of reasoning we have arrived at an absurd conclusion. This is paradoxical. Thus, is ‘mere’ addition innocuous, as is here assumed? Well, if it is thought to be suspicious, there is a way of avoiding it by starting with a population like the one in A and adding new people living at a slightly lower level than the people in A in a manner that increases the well-being of existing people. You then proceed down the moral alphabet by levelling out the well-being between the best and worst off in a manner that gives more to those who are worst off than you take from those who are best off; in each step new people are added, in order to make this change of the situation possible (Parfit 1984; Tännsjö 2002). Moreover, there are other abstract arguments leading in the same direction, some of them presented by Parfit himself (Parfit 1984; Arrhenius 2000a, b; Kitcher 2000; Rachels 2004). It seems then that the Repugnant Conclusion is very hard to get around.

The main challenge which Parfit presented in his celebrated work Reasons and Persons is to develop a theory of beneficence – theory X he calls it—which is able to solve the Non-identity problem, which does not lead to the Repugnant Conclusion and which thus manages to block the Mere Addition Paradox, without facing other morally unacceptable conclusions. However, Parfit’s own conclusion was that he had not succeeded in developing such a theory.

It might be tempting for people who have little sympathy with utilitarian thought to try to set the problems raised by the Repugnant Conclusion to one side, thinking that it constitutes a problem only for utilitarians. However, most people tend to believe that we have some obligation to make the world a better place, at least if we can do so without violating any deontological constraints, and at a not too high cost to ourselves. Clearly all who think along these lines, even without being utilitarians, are faced with the problem of the Repugnant Conclusion. We can assume that other values and considerations are not decisive for the choice between populations A and Z in Fig. 1 (e.g., promises, rights). The Repugnant Conclusion is a problem for all moral theories which hold that welfare at least matters when all other things are equal.”—from Gustaf Arrhenius, Jesper Ryberg, and Torbjorn Tannsjo, “The Repugnant Conclusion,” Stanford Encyclopedia of Philosophy,

For more information, see

Tyler Cowen, “What Do We Learn From the Repugnant Conclusion?”


  1. Samuel Scheffler on Life after Death

“Consider a hypothetical scenario. Suppose you knew that although you yourself would live a long life and die peacefully in your sleep, the earth and all its inhabitants would be destroyed 30 days after your death in a collision with a giant asteroid. How would this knowledge affect you?

If you are like me, and like most people with whom I have discussed the question, you would find this doomsday knowledge profoundly disturbing. And it might greatly affect your decisions about how to live. If you were a cancer researcher, you might be less motivated to continue your work. (It would be unlikely, after all, that a cure would be found in your lifetime, and even it were, how much good would it do in the time remaining?) Likewise if you were an engineer working to improve the seismic safety of bridges, or an activist trying to reform our political or social institutions or a carpenter who cared about building things to last. What difference would these endeavors make, if the destruction of the human race was imminent?

If you were a novelist or playwright or composer, you might see little point in continuing to write or compose, since these creative activities are often undertaken with an imagined future audience or legacy in mind. And faced with the knowledge that humanity would cease to exist soon after your death, would you still be motivated to have children? Maybe not.

Notice that people do not typically react with such a loss of purpose to the prospect of their own deaths. Of course, many people are terrified of dying. But even people who fear death (and even those who do not believe in a personal afterlife) remain confident of the value of their activities despite knowing that they will die someday. Thus there is a way in which the survival of other people after our deaths matters more to us than our own survival.

The explanation for this may seem simple: if the earth will be destroyed 30 days after we die, then everyone we care about who is alive at that time will meet a sudden, violent end. Spouses and partners, children and grandchildren, friends and lovers: all would be doomed. Perhaps it is our concern for our loved ones that explains our horror at the prospect of a post-mortem catastrophe.

But I don’t think this is the full story. Consider another hypothetical scenario, drawn from P. D. James’s novel “The Children of Men.” In Ms. James’s novel, humanity has become infertile, with no recorded birth having occurred in over 25 years. Imagine that you found yourself living in such circumstances. Nobody now alive is younger than 25, and the disappearance of the human race is imminent as an aging population inexorably fades away. How would you react?

As in the case of the asteroidal collision, many activities would begin to seem pointless under these conditions: cancer research, seismic safety efforts, social and political activism and so on. Beyond that, as Ms. James’s novel vividly suggests, the onset of irreversible global infertility would be likely to produce widespread depression, anxiety and despair.

Some people would seek consolation in religious faith, and some would find it. Others would take what pleasure they could in activities that seemed intrinsically rewarding: listening to music, exploring the natural world, spending time with family and friends and enjoying the pleasures of food and drink. But even these activities might seem less fulfilling, and be tinged with sadness and pain, when set against the background of a dying humanity.

NOTICE that in this scenario, unlike that of the asteroidal collision, nobody would die prematurely. So what is dismaying about the prospect of living in an infertile world cannot be that we are horrified by the demise of our loved ones. (They would die eventually, of course, but that is no different from our actual situation.) What is dismaying is simply that no new people would come into existence.

This should give us pause. The knowledge that we and everyone we know and love will someday die does not cause most of us to lose confidence in the value of our daily activities. But the knowledge that no new people would come into existence would make many of those things seem pointless.

I think this shows that some widespread assumptions about human egoism are oversimplified at best. However self-interested or narcissistic we may be, our capacity to find purpose and value in our lives depends on what we expect to happen to others after our deaths. Even the egotistic tycoon who is devoted to his own glory might discover that his ambitions seemed pointless if humanity’s disappearance was imminent. Although some people can afford not to depend on the kindness of strangers, virtually everyone depends on the future existence of strangers.”—from Samuel Scheffler, “The Importance of the Afterlife, Seriously,”


For more information, see

“A Philosopher’s Afterlife: We May Die, but Others Live On,” NPR,